C4 chapter 4 - differentiation

In this chapter you will learn how to:

• find the gradient of a curve with an equation that is given in parametric form
• differentiate implicit functions and relations
• differentiate exponential growth and decay functions
• relate the rate of change of one variable to the rate of change of another to which it is connected

Sections

C4 section 4.1

You need to be able to find the gradient of a curve given in parametric form.

You need to know that if you have x = f(t) and y = g(t) you can find dy/dx by using the chain rule:
$\displaystyle \frac {dy} {dx} = \frac {dy} {dt} \times \frac {dt} {dx} \implies \frac {dy} {dx} = \frac {dy} {dt} \div \frac {dx} {dt} \implies \frac {dy} {dx} = g'(t) \div f'(t)$


Examples:
Find the gradient at the point P where t = 1 on the curve which is produced by the parametric relations x = t³ + 2t and y = t² - 1
So you can imagine what's going on, here's the graph:

C4 Exercise 4A

• C4 Exercise 4A worked solutions (partially complete - as usual, ask on the Sandbox if you need something particular):
  

  C4 Exercise 4A (gradients of parametric curves).jnt
  

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C4 section 4.2

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C4 Exercise 4B

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C4 section 4.3

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C4 Exercise 4C

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C4 section 4.4

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C4 Exercise 4D

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